Time of Year/Month – 5 to 6 weeks after winter break (approx. month February)
Instructional Purpose
Unit Title: Quadratics
Learning Objectives: Content: Solve quadratic equations by graphing. Solve quadratic equations by factoring. Language: Work in a group and practice communication skills. Write a simple paragraph when given a prompt. Read directions and follow the multiple steps to fill out a quiz.
CA Content standards that are the target of student learning:
California Math Standard Algebra 1 - 21.0 Students graph quadratic functions and know that their roots are the x-intercepts California Math Standard Algebra 1 - 14.0 Students solve a quadratic equation by factoring
Formal and Informal assessments:
Warm-up Activity – review on plotting points on a graph paper with an x and y axis (Informal) Class Discussion of similarities and differences between graphed parabola examples (Informal) Warm-up Quiz – key vocabulary terms for a parabola (Formal) Free write on similarities and differences between graphing and factoring quadratic equations. (Informal)
Instructional Activities and Resources.
1. Do Warm-up Activity (informal) (5 minutes) Plot a series of given points on a piece of graph paper with an x and y axis. Identify the function as a parabola. Pocket Question: Label all the components of this graph using the following key words (axis of symmetry, vertex, roots, solutions, zeros, x-intercepts, y-intercepts, maximum, minimum)
2. Grade Warm-up Activity (10 minutes) Students will exchange papers with their partners and grade their partner’s warm-up. Display a graph of the plotted points. Teacher asks the question: “What do the plotted points represent? Tell your partner.” Have a student share out and discuss what a parabola is. Key phrase is “Quadratic Equation”.
List words up on the board from pocket question and perform a silent activity. This is where students are not allowed to speak and they are to complete the task of labeling the parabola displayed on the board with the terms from the word bank. The activity begins with a volunteer who puts a word next to the appropriate part of the parabola, then the student who just volunteered hands the marker to another student of their choice to perform the same task using another word from the word bank. This process repeats itself without speaking until all the words that can be used to label the parabola are depleted.
3. Graph Quadratic Equation Examples (25 minutes) A. x ^2 + 7x + 10 = 0 (Two negative roots) Change the “0” to a “y” Demonstrate to the students the process of picking a series of x values and putting them into an x-y chart. After selecting a series of x values for the x-y chart - substitute the x values into the given quadratic equation and solve to obtain a corresponding y value This process will give you a point to plot on a graph with an x and y axis The group of points will create a graph of a parabola. B. x^2 + 2x – 8 = 0 (One negative root and one positive root) This example will be done by the students using the first example as a guide. The students will be allowed to work with a partner. I will circulate the class and check for understanding. Pocket Question: For students who finish early, I will ask them to label their parabola with the same bank of words from the warm up activity.
Have the class do examples C and D with their partners. Continue to label all parabolas with the key terms that apply to each example from the word bank. C. x^2 + 6x + 9 = 0 (One root) D. x^2 + 2x + 10 = 0 (No root)
If students finish early they will begin their homework. Textbook Page 567 (21-26 all)
4. Discuss 4 parabola examples (13 minutes) Pose the question to the class – “Describe using academic language what parts of the parabola are similar and what parts are different between the two parabolas that were just graphed” I will write responses on the board that describes the similarities and differences.
Break: Mandatory 6 minute passing period (not part of instructional time)
5. Go to the computer lab. Do Warm-up Quiz (formal) (5 minutes) This quiz will be checking for understanding of key vocabulary for a parabola. The quiz will be given to every student and they would be required to work alone. If they finish before time is up then they can turn the quiz over and begin or continue with their homework problems.
6. Give Feedback on Warm-up Quiz (3 minutes) Display a copy of the parabola on the Smartboard. Have volunteer students label the parabola on the Smartboard. Have the students raise their hands that got all 8 terms correctly labeled on the parabola. Quickly identify the students that are not raising their hands and take a mental note to give them additional support during group work period.
7. Do Group Powerpoint Activity (35 minutes) Have students arrange themselves in pre-assigned groups. Introduce the procedure to scan a document into the computer and paste the graphic into a Powerpoint slide. Allow students to design a Powerpoint presentation to show work performed in the first half of class. Each group must produce a minimum of 10 slides (introduction, 2 slides for each example and a conclusion).
8. Write about the Powerpoint Activity (10 minutes) Give the students the prompt: What similarities can you see between the factoring solutions and x intercepts of Examples A, B and C? Please explain your reasoning. What happened in Example D? Is it different from the rest of the examples? Explain in what way? What technology problems did you encounter? How did you scan your graphs and show your work in your Powerpoint slides?
Time of Year/Month – 5 to 6 weeks after winter break (approx. month February)
Instructional Purpose
Unit Title: Quadratics
Learning Objectives: Content: Use algebra tiles to model completing the square. Language: Work in groups with other students to practice communication skills. Read directions and follow the multiple steps to fill out a worksheet.
Content standards that are the target of student learning:
California Math Standard Algebra 1 - 14.0 Students solve a quadratic equation by completing the square.
Formal and Informal assessments: Discuss previous day’s homework assignment. (Informal)
Instructional Strategies and Learning Tasks to Support Student Learning.
1. Review Homework Problems from previous day (13 minutes)
“The height of a diver above the water during a dive can be modeled by h = -16t^2 + 8t + 48, where h is height in feet and t is time in seconds. Find the time it takes for the diver to reach the water.” (California Holt Algebra 1 page 578 Example 3)
“A group of friends tries to keep a beanbag from touching the ground with using their hands. Once the beanbag has been kicked, its height can be modeled by h = -16t^2 + 14t + 2, where h is the height in feet above the ground and t is the time in seconds. Find the time it takes the beanbag to reach the ground.” (California Holt Algebra 1 page 579 Problem 19)
Discuss various approaches that students took. Answer questions to identify problem areas to address.
2. Model Completing the Square Activity (40 minutes)
We will use a worksheet I created by using California Holt Algebra 1 page 590 as a guide. Students will be seated in groups of four for this activity.
The worksheet is divided into three segments: A. Activating Prior Knowledge The students are given a prompt that has them describe what they know about the characteristics of a square. While the students are writing, I will pass out Algebra Tiles for each group to work with B. Concept Development Have the students “fill in the missing parts” of a diagram on their worksheets. They will see that the diagram can be filled in with “unit algebra tiles”. I will circulate around the classroom to assist the groups in completing the task and ensure that they visualize this task as “completing the square” C. Skill Development and Guided Practice I will do an example problem to model the procedure necessary to do the guided practice problems The groups will be assigned problems from the text (California Holt Algebra 1 Page 590 1-5 all)
Break: Mandatory 6 minute passing period (not part of instructional time)
3. Go to the computer lab. (30 minutes) Arrange class in predetermined groups. Have each group find three YouTube videos that demonstrate the use of completing the square method for solving quadratics. Each video must be accompanied by a one paragraph summary.
4. Share findings with entire class. (23 minutes) Each group will select the best video of their three YouTube video clips with the class. They will highlight what the clip contains and why they felt it was the best video clip.
Competency Lesson - Powerpoint
Instructional ContextInstructional Purpose
- Unit Title: Quadratics
- Learning Objectives: Content: Solve quadratic equations by graphing. Solve quadratic equations by factoring. Language: Work in a group and practice communication skills. Write a simple paragraph when given a prompt. Read directions and follow the multiple steps to fill out a quiz.
- CA Content standards that are the target of student learning:
California Math Standard Algebra 1 - 21.0Students graph quadratic functions and know that their roots are the x-intercepts
California Math Standard Algebra 1 - 14.0
Students solve a quadratic equation by factoring
- Formal and Informal assessments:
Warm-up Activity – review on plotting points on a graph paper with an x and y axis (Informal)Class Discussion of similarities and differences between graphed parabola examples (Informal)
Warm-up Quiz – key vocabulary terms for a parabola (Formal)
Free write on similarities and differences between graphing and factoring quadratic equations. (Informal)
Instructional Activities and Resources.
1. Do Warm-up Activity (informal) (5 minutes)
Plot a series of given points on a piece of graph paper with an x and y axis.
Identify the function as a parabola.
Pocket Question: Label all the components of this graph using the following key words (axis of symmetry, vertex, roots, solutions, zeros, x-intercepts, y-intercepts, maximum, minimum)
2. Grade Warm-up Activity (10 minutes)
Students will exchange papers with their partners and grade their partner’s warm-up.
Display a graph of the plotted points.
Teacher asks the question: “What do the plotted points represent? Tell your partner.”
Have a student share out and discuss what a parabola is. Key phrase is “Quadratic Equation”.
List words up on the board from pocket question and perform a silent activity. This is where students are not allowed to speak and they are to complete the task of labeling the parabola displayed on the board with the terms from the word bank. The activity begins with a volunteer who puts a word next to the appropriate part of the parabola, then the student who just volunteered hands the marker to another student of their choice to perform the same task using another word from the word bank. This process repeats itself without speaking until all the words that can be used to label the parabola are depleted.
3. Graph Quadratic Equation Examples (25 minutes)
A. x ^2 + 7x + 10 = 0 (Two negative roots)
Change the “0” to a “y”
Demonstrate to the students the process of picking a series of x values and putting them into an x-y chart.
After selecting a series of x values for the x-y chart - substitute the x values into the given quadratic equation and solve to obtain a corresponding y value
This process will give you a point to plot on a graph with an x and y axis
The group of points will create a graph of a parabola.
B. x^2 + 2x – 8 = 0 (One negative root and one positive root)
This example will be done by the students using the first example as a guide.
The students will be allowed to work with a partner.
I will circulate the class and check for understanding.
Pocket Question: For students who finish early, I will ask them to label their parabola with the same bank of words from the warm up activity.
Have the class do examples C and D with their partners. Continue to label all parabolas with the key terms that apply to each example from the word bank.
C. x^2 + 6x + 9 = 0 (One root)
D. x^2 + 2x + 10 = 0 (No root)
If students finish early they will begin their homework.
Textbook Page 567 (21-26 all)
4. Discuss 4 parabola examples (13 minutes)
Pose the question to the class – “Describe using academic language what parts of the parabola are similar and what parts are different between the two parabolas that were just graphed”
I will write responses on the board that describes the similarities and differences.
Break: Mandatory 6 minute passing period (not part of instructional time)
5. Go to the computer lab.
Do Warm-up Quiz (formal) (5 minutes)
This quiz will be checking for understanding of key vocabulary for a parabola.
The quiz will be given to every student and they would be required to work alone.
If they finish before time is up then they can turn the quiz over and begin or continue with their homework problems.
6. Give Feedback on Warm-up Quiz (3 minutes)
Display a copy of the parabola on the Smartboard.
Have volunteer students label the parabola on the Smartboard.
Have the students raise their hands that got all 8 terms correctly labeled on the parabola.
Quickly identify the students that are not raising their hands and take a mental note to give them additional support during group work period.
7. Do Group Powerpoint Activity (35 minutes)
Have students arrange themselves in pre-assigned groups. Introduce the procedure to scan a document into the computer and paste the graphic into a Powerpoint slide. Allow students to design a Powerpoint presentation to show work performed in the first half of class. Each group must produce a minimum of 10 slides (introduction, 2 slides for each example and a conclusion).
8. Write about the Powerpoint Activity (10 minutes)
Give the students the prompt: What similarities can you see between the factoring solutions and x intercepts of Examples A, B and C? Please explain your reasoning. What happened in Example D? Is it different from the rest of the examples? Explain in what way? What technology problems did you encounter? How did you scan your graphs and show your work in your Powerpoint slides?
Resources and Materials:
California Holt Algebra 1 Textbook 2008
Dry Erase Markers
Computer Lab
Smartboard
LCD projector
Teacher prepared Warm-up Activity
Teacher prepared Warm-up Quiz
Resource Lesson - YouTube
Instructional ContextInstructional Purpose
- Unit Title: Quadratics
- Learning Objectives: Content: Use algebra tiles to model completing the square. Language: Work in groups with other students to practice communication skills. Read directions and follow the multiple steps to fill out a worksheet.
- Content standards that are the target of student learning:
California Math Standard Algebra 1 - 14.0Students solve a quadratic equation by completing the square.
Instructional Strategies and Learning Tasks to Support Student Learning.
1. Review Homework Problems from previous day (13 minutes)
“The height of a diver above the water during a dive can be modeled by h = -16t^2 + 8t + 48, where h is height in feet and t is time in seconds. Find the time it takes for the diver to reach the water.” (California Holt Algebra 1 page 578 Example 3)
“A group of friends tries to keep a beanbag from touching the ground with using their hands. Once the beanbag has been kicked, its height can be modeled by h = -16t^2 + 14t + 2, where h is the height in feet above the ground and t is the time in seconds. Find the time it takes the beanbag to reach the ground.” (California Holt Algebra 1 page 579 Problem 19)
Discuss various approaches that students took.
Answer questions to identify problem areas to address.
2. Model Completing the Square Activity (40 minutes)
We will use a worksheet I created by using California Holt Algebra 1 page 590 as a guide.
Students will be seated in groups of four for this activity.
The worksheet is divided into three segments:
A. Activating Prior Knowledge
The students are given a prompt that has them describe what they know about the characteristics of a square.
While the students are writing, I will pass out Algebra Tiles for each group to work with
B. Concept Development
Have the students “fill in the missing parts” of a diagram on their worksheets. They will see that the diagram can be filled in with “unit algebra tiles”.
I will circulate around the classroom to assist the groups in completing the task and ensure that they visualize this task as “completing the square”
C. Skill Development and Guided Practice
I will do an example problem to model the procedure necessary to do the guided practice problems
The groups will be assigned problems from the text (California Holt Algebra 1 Page 590 1-5 all)
Break: Mandatory 6 minute passing period (not part of instructional time)
3. Go to the computer lab. (30 minutes)
Arrange class in predetermined groups. Have each group find three YouTube videos that demonstrate the use of completing the square method for solving quadratics. Each video must be accompanied by a one paragraph summary.
4. Share findings with entire class. (23 minutes)
Each group will select the best video of their three YouTube video clips with the class. They will highlight what the clip contains and why they felt it was the best video clip.
Resources and Materials:
California Holt Algebra 1 Textbook 2008
Smartboard
Computer Lab
Dry Erase Markers
Algebra Tiles
Teacher prepared worksheet “Model Completing the Square”